In recent years, stylized forms of the Boltzmann equation, now going by the name of "Lattice Boltzmann equation" (LBE), have emerged, which relinquish most mathematical complexities of the true Boltzmann equation without sacrificing physical fidelity in the description of many situations involving complex fluid motion. This book provides the first detailed survey of LBE theory and its major applications to date. Accessible to a broad audience of scientists dealing with complex system dynamics, the book also portrays future developments in allied areas of science (material science, biology etc.) where fluid motion plays a distinguished role.